Ever increasingly huge sets of data indexed with reference to 2d, 3d or 4d real space are being collected in all fields of science and require intelligent data models for weil performing management. Thus we experience a growing interest in more efficient data models to describe objects, both in terms of memory and management, especially search and retrieval.Two features involve modeling objects: geometry and topology. The former gives the description about the location in space, the shape of objects. The latter describes the neighboring relationships between objects, and that between cells (ie. vertices, edges, faces, etc) of objects.The contributions of this work can be summarized into the following aspects:- Defining the decomposition of objects into cells, and properties of such a decomposition;- A novel model for modeling the topology of objects given in any spatial dimension;- An approach for converting objects given in terms of pixel or voxel into boundary representation including topology;- An application in Materials science to reconstruct grain boundaries from Electron backscatter diffraction data;